Brian Keith-Norambuena

Brian Keith-Norambuena, Juan Bekios-Calfa

We provide a unified theoretical analysis of Linear Discriminant Analysis with simultaneous multilabel scatter matrix formulations and Stiefel orthogonality constraints. Our contributions span both algebraic structure and statistical guarantees. On the algebraic side, we characterize the rank of the multilabel between-class scatter matrix, showing that the effective discriminant dimensionality can strictly exceed the classical single-label bound of $C-1$; we establish a multilabel partition of variance and prove that all four Fisher objectives are equivalent under the $W^\top S_t^{ML} W = I_r$ constraint while characterizing their divergence under the Stiefel constraint; and we prove a two-sided label-distance preservation bound relating projected distances to Hamming distances in label space. On the statistical side, we establish a finite-sample $O(k_{\max}\sqrt{d\log d/n}/gap_r)$ bound on the subspace estimation error under sub-Gaussian noise with a matching $Ω(σ^2 d/(n\,gap_r))$ minimax lower bound, establishing a near-minimax-optimal rate (matching up to logarithmic and $k_{\max}$ factors) for multilabel discriminant subspace estimation. We further provide high-probability distance concentration, robustness guarantees under label interactions, and a regularization analysis preserving the spectral structure when $d \gg n$. All results are verified numerically on synthetic data generated from the linear label-effect model, covering both the algebraic identities and the multilabel-specific quantities ($k_{\max}$, $κ(S_t^{ML})$, $\|Γ/n\|_2$, $Δ_r$) that govern the statistical bounds. The numerical experiments are designed as a sanity check for the theorems rather than as an empirical benchmark; evaluation on real multilabel datasets is left to future work targeting application-oriented venues.

Brian Keith-Norambuena

Visualization's design knowledge-effectiveness rankings, encoding guidelines, color models, preattentive processing rules -- derives from six decades of psychophysical studies of human vision. Yet vision-language models (VLMs) increasingly consume chart images in automated analysis pipelines, and a growing body of benchmark evidence indicates that this human-centered knowledge base does not straightforwardly transfer to machine audiences. Machines exhibit different encoding performance patterns, process images through patch-based tokenization rather than holistic perception, and fail on design patterns that pose no difficulty for humans-while occasionally succeeding where humans struggle. Current approaches address this gap primarily by bypassing vision entirely, converting charts to data tables or structured text. We argue that this response forecloses a more fundamental question: what visual representations would actually serve machine cognition well? This paper makes the case that the visualization field needs to investigate machine-oriented visual design as a distinct research problem. We synthesize evidence from VLM benchmarks, visual reasoning research, and visualization literacy studies to show that the human-machine perceptual divergence is qualitative, not merely quantitative, and critically examine the prevailing bypassing approach. We propose a conceptual distinction between human-oriented and machine-oriented visualization-not as an engineering architecture but as a recognition that different audiences may require fundamentally different design foundations-and outline a research agenda for developing the empirical foundations the field currently lacks: the beginnings of a "machine Bertin" to complement the human-centered knowledge the field already possesses.